Answer:
The probability that a randomly selected resident of the Gold dorm is a senior is 0.1562
Step-by-step explanation:
The given percentage of each class of student is presented as follows;
Priority A (seniors) = 22%, ∴ P(s) = 0.22
Priority B (juniors) = 29%, ∴ P(j) = 0.29
Priority C (freshmen and sophomores) = (100 - 22 - 29)% = 49%, ∴ P(fs) = 0.49
The percentage of the seniors that elect to live at the Gold dorm, = 71%, ∴ P(sG) = 0.71
The percentage of the juniors that live at the Gold dorm = 19%, ∴ P(jG) = 0.19
The percentage of the freshmen and sophomores that live in the Gold dorm = 5%, ∴ P(fsG) = 0.05
The probability that a randomly selected resident of the Gold dorm is a senior = P(s∩sG) = P(s) × P(sG)
∴ P(s∩sG) = 0.22 × 0.71 = 0.1562
Therefore;
The probability that a randomly selected resident of the Gold dorm is a senior = P(s∩sG) = 0.1562.
